It appears that at the present if you have a Picasa Web Album that is not set public it may appear in the list of albums available to insert into your site using Insert>>Google+>>Photo Album but it will not appear in the site until you go to Picasa Web Albums to set the sharing to "Public on the Web.
It is not possible to make it public in Google Photos.
NOTE: This no longer works. You are redirected to Google Photos where you can create a "Shared Album" but there is no option to make it public, only limited to anyone with the link. When such an album is inserted in a page it is visible only to viewers when they are signed in with a Google account.
This problem has been reported to Google.